Course Description
Open to: Grades 11, 12 One Year Course
Prerequisite: Intermediate Algebra 1, Instructor/Counselor
Approval
Content: Students will study extended concepts of algebra,
geometry and probability with an emphasis on geometry
and introductory advanced algebra using an integrated
approach.
Adopted Materials
Title: Geometry: Tools For A Changing World
Edition: 1998
Publisher: Prentice-Hall, Inc.
ISBN: 0-13-411067-6
Mathematics Curriculum
Map
Course overview, activities, vocabulary, supplemental
materials in pdf format.
Copyright
Resources
Course Scope
| Unit
1 |
Tools of Geometry |
3 weeks |
| Unit
2 |
Investigating Geometric Figures |
3 weeks |
| Unit
3 |
Triangle Relationships |
2 weeks |
| Unit
4 |
Planar Measurement |
3 weeks |
| Unit
5 |
Spatial Measurement |
3 weeks |
| Unit
6 |
Reasoning and Parallel Lines |
2 weeks |
| Unit
7 |
Transformations |
2 weeks |
| Unit
8 |
Proving Triangle Congruent |
2 weeks |
| Unit
9 |
Quadrilaterals |
2 weeks |
| Unit
10 |
Similarity |
4 weeks |
| Unit
11 |
Right Triangle Trigonometry |
3 weeks |
| Unit
12 |
Chords, Secants, and Tangents |
4 weeks |
Assessment
Correlation acronyms key
Mathematics Curriculum Matrix K-12 pdf or Word
document
|
Unit
1 |
Tools of Geometry |
3 weeks |
|
Instructional Objective
0825.01 Understand and apply basic geometric
concepts. |
Standard Reference
|
|
No.
|
Performance Objective
|
Resource Reference
|
Assessment Correlation
|
|
01 |
Use inductive reasoning to describe patterns. |
p. 5 |
TMA |
|
02 |
Describe the relationships between points, lines
and planes. |
pp. 13, 14, 18, 19 |
TMA |
|
03 |
Define and apply terms and notation associated
with lines and planes. |
pp. 18, 19 |
EOC, TMA |
|
04 |
Find the length of a segment. |
p.25 |
EOC, TMA |
|
05 |
Measure and classify angles. |
pp. 27, 28 |
EOC, TMA |
|
06 |
Apply angle/segment addition. |
pp. 26, 28 |
EOC, TMA |
|
07 |
Understand and apply basic geometric terms.
(midpoint, perpendicular lines, perpendicular
bisector and angle bisector) |
pp. 33, 34 |
EOC, TMA |
|
08 |
Construct, using a straightedge and compass,
a two-dimensional figure from a set of instructions. |
pp. 40, 42 |
EOC, TMA |
|
09 |
Identify special angle relationships (vertical,
adjacent, complementary, and supplementary). |
p. 48 |
EOC, TMA |
|
10 |
Find numerical unknowns related to the coordinate
plane (distance and midpoint) |
pp. 54, 55 |
EOC, TMA |
|
Back to Top |
|
Unit
2 |
Investigating Geometric
Figures |
3 weeks |
|
Instructional Objective
0825.02 Expand the understanding of basic
geometric concepts by investigating shapes. |
Standard Reference
|
|
No.
|
Performance Objective
|
Resource Reference
|
Assessment Correlation
|
|
01 |
Relate the measures of interior and exterior
angles of a triangle (sum of the interior angles,
remote exterior angles). |
pp. 68-70 |
EOC, TMA |
|
02 |
Classify triangles by their angle measure and
side length. |
p. 71 |
EOC, TMA |
|
03 |
Classify polygons (convex, concave, equilateral,
equiangular and regular). |
pp. 76, 78 |
EOC, TMA |
|
04 |
Find the measure of the angles of a polygon
and the sum of the interior and exterior angles
of a polygon. |
pp. 77, 78 |
EOC, TMA |
|
05 |
Graph lines in the coordinate plane. |
p. 84 |
EOC, TMA |
|
06 |
Classify lines as parallel or perpendicular
by their slopes. |
p. 85 |
EOC, TMA |
|
07 |
Define and classify special quadrilaterals. |
p. 91 |
EOC, TMA |
|
08 |
Use vocabulary associated with circles (circle,
radius, diameter, central angle, semicircle,
minor arc, major arc, adjacent arcs). |
pp. 96-98 |
EOC, TMA |
|
09 |
Find the measure of arcs and central angles
of circles. |
p. 98 |
EOC, TMA |
|
10 |
Display data in a circle graph. |
p. 99 |
EOC, TMA |
|
11 |
Differentiate between similar and congruent
figures. |
pp. 102-103 |
EOC, TMA |
|
12 |
Draw isometric and orthographic views of objects. |
pp. 110-111 |
TMA |
|
Instructional Objective
0825.03 Understand and use a variety of reasoning
and problem solving skills. |
Standard Reference
|
|
No.
|
Performance Objective
|
Resource Reference
|
Assessment Correlation
|
|
01 |
Define and apply terms associated with conditional
statements and mathematical reasoning. |
pp. 182-184 |
EOC, TMA |
|
02 |
Apply properties of isosceles triangles. |
p. 189 |
EOC, TMA |
|
03 |
Define mid-segment and apply its properties. |
p. 201 |
EOC, TMA |
|
04 |
Apply triangle inequalities to solve problems. |
pp. 213-215 |
EOC, TMA |
|
05 |
Apply properties of bisectors (angle and perpendicular). |
p. 219 |
EOC, TMA |
|
06 |
Define and apply intersections of special segments
of a triangle (median, altitude, angle bisector,
and perpendicular bisector). |
pp. 227-230 |
EOC, TMA |
|
Instructional Objective
0825.04 Use formulas to determine planar measurements
of polygons and circles. |
Standard Reference
|
|
No.
|
Performance Objective
|
Resource Reference
|
Assessment Correlation
|
|
01 |
Calculate the area and perimeter of rectangles. |
pp. 243-244 |
EOC, TMA |
|
02 |
Calculate the area of triangles and parallelograms. |
pp. 249-251 |
EOC, TMA |
|
03 |
Simplify radicals. |
p. 255 |
EOC, TMA |
|
04 |
Find the missing side lengths of a right triangle
using the Pythagorean Theorem. |
p.257 |
EOC, TMA |
|
05 |
Classify a triangle as obtuse, acute or right
by applying the converse of the Pythagorean Theorem. |
p. 258 |
EOC, TMA |
|
06 |
Apply the properties of special right triangles
(30-60-90 & 45-45-90). |
pp. 263-265 |
EOC, TMA |
|
07 |
Calculate the area of a trapezoid. |
p. 269 |
EOC, TMA |
|
08 |
Calculate the area of a regular polygon. |
p. 274 |
EOC, TMA |
|
09 |
Solve problems involving arc length of a circle. |
pp. 279-281 |
EOC, TMA |
|
10 |
Calculate the areas of circles, sectors and
segments of circles. |
pp. 285-287 |
EOC, TMA |
|
Instructional Objective
0825.05 Perform calculations for surface area
and volume of three dimensional figures. |
Standard Reference
|
|
No.
|
Performance Objective
|
Resource Reference
|
Assessment Correlation
|
|
01 |
Identify vocabulary associated with spatial
figures. |
pp. 302, 309-311, 316, 318. 340. |
EOC, TMA |
|
02 |
Calculate the surface area of prisms and cylinders. |
pp. 310-311 |
EOC, TMA |
|
03 |
Calculate the surface area of pyramids and cones. |
pp. 317-318 |
EOC, TMA |
|
04 |
Calculate the volumes of prisms and cylinders. |
pp. 324-325 |
EOC, TMA |
|
05 |
Calculate the volumes of pyramids and cones. |
pp. 331-332 |
EOC, TMA |
|
06 |
Calculate the surface area and volume of spheres. |
pp. 339-340 |
EOC, TMA |
|
07 |
Calculate the volume of composite space figures. |
pp. 344-345 |
EOC, TMA |
|
08 |
Calculate geometric probability. |
pp. 348-350 |
EOC, TMA |
|
Back to Top |
|
Unit
6 |
Reasoning and Parallel
Lines |
2 weeks |
|
Instructional Objective
0825.06 Deduce the parallel/perpendicular
relationship between lines through calculations
and constructions. |
Standard Reference
|
|
No.
|
Performance Objective
|
Resource Reference
|
Assessment Correlation
|
|
01 |
Identify and calculate the measure of angles
formed by two parallel lines and a transversal. |
pp. 363-364 |
EOC, TMA |
|
02 |
Establish if two lines are parallel. |
pp. 371-372 |
EOC, TMA |
|
03 |
Construct parallel and perpendicular lines. |
pp. 377-380 |
EOC, TMA |
|
04 |
Draw objects in one-and two point perspective. |
pp. 386-387 |
TMA |
|
Instructional Objective
0825.07 Use coordinate geometry to solve problems
involving transformations. |
Standard Reference
|
|
No.
|
Performance Objective
|
Resource Reference
|
Assessment Correlation
|
|
01 |
Identify the result of a specific transformation
or kind of transformation used to create a given
result. |
p.124-177, 371,144-150, 175-176 |
EOC, TMA |
|
02 |
Relate line symmetry to reflections. |
p. 125-130, 151, 174 |
EOC, TMA |
|
03 |
Relate rotational symmetry and rotations. |
p. 138-143, 175 |
EOC, TMA |
|
04 |
Find magnitudes and directions of vectors. |
p. 133-137 |
EOC, TMA |
|
Instructional Objective
0825.08 Describe, classify and prove relationships
between triangles. |
Standard Reference
G.2.2.2a,b, G.4.1.1d,f,g,i,, G.4.1.2a, G.4.1.3c |
|
No.
|
Performance Objective
|
Resource Reference
|
Assessment Correlation
|
|
01 |
Identify and classify triangles by their angle
measure and side lengths. (e.g., acute, obtuse,
right, scalene, isosceles, equilateral.) |
p. 263-268 |
EOC, TMA |
|
02 |
Find angles related to triangles-interior/exterior. |
p. 69-70, 117, 615 |
EOC, TMA |
|
03 |
Describe and apply the congruence relationships.
for triangles (e.g., SSS, SAS, ASA, AAS, HL.) |
p. 406-438, 441-443 |
EOC, TMA |
|
04 |
Use CPCTC in congruence relationships. |
pp. 102 |
EOC, TMA |
|
Instructional Objective
0825.07 Apply properties of quadrilaterals. |
Standard Reference
|
|
No.
|
Performance Objective
|
Resource Reference
|
Assessment Correlation
|
|
01 |
Apply the properties of parallelograms. |
pp. 448-450 |
EOC, TMA |
|
02 |
Determine if a quadrilateral is a parallelogram. |
pp. 456 |
EOC, TMA |
|
03 |
Apply properties of special parallelograms (rectangles,
rhombuses and squares). |
pp. 463-464 |
EOC, TMA |
|
04 |
Apply properties of trapezoids and kites. |
pp. 470-471 |
EOC, TMA |
|
05 |
Use coordinate geometry to prove statements. |
pp. 483-484 |
TMA |
|
Instructional Objective
0825.10 Use ratio and proportions to solve
problems involving similar shapes. |
Standard Reference
|
|
No.
|
Performance Objective
|
Resource Reference
|
Assessment Correlation
|
|
01 |
Use ratio and proportion in similarity problems. |
pp. 496-498 |
EOC, TMA |
|
02 |
Solve for parts of right triangles using the
geometric mean. |
pp. 511-512 |
EOC, TMA |
|
03 |
Solve problems in triangles using proportionality. |
pp. 517-519 |
EOC, TMA |
|
04 |
Use proportions to find perimeters and areas
of similar figures. |
pp. 525,532 |
EOC, TMA |
|
Back to Top |
|
Unit
11 |
Right Triangle Trigonometry |
3 weeks |
|
Instructional Objective
0825.11Apply trigonometry ratios to right
triangles and add vectors. |
Standard Reference
|
|
No.
|
Performance Objective
|
Resource Reference
|
Assessment Correlation
|
|
01 |
Calculate tangent ratios in right triangles. |
p. 544 |
EOC, TMA |
|
02 |
Calculate sine and cosine ratios in right triangles. |
p. 551 |
EOC, TMA |
|
03 |
Apply trigonometry ratios to find missing lengths
or angle measures of right triangles. |
pp. 544-546, 551-553 |
EOC, TMA |
|
04 |
Solve right triangle problems involving angles
of elevation and depression. |
p. 556 |
EOC, TMA |
|
05 |
Calculate the magnitude and direction of vectors. |
p. 563 |
EOC, TMA |
|
06 |
Add vectors to solve problems. |
p. 568 |
EOC, TMA |
|
07 |
Apply trigonometry to find areas. |
pp. 573-575 |
EOC, TMA |
|
Back to Top |
|
Unit
12 |
Chords, Secants, and
Tangents |
4 weeks |
|
Instructional Objective
0825.10 Apply properties of chords, secants
and tangents to solve problems. |
Standard Reference
|
|
No.
|
Performance Objective
|
Resource Reference
|
Assessment Correlation
|
|
01 |
Write and apply the equation of a circle. |
p. 586 |
EOC, TMA |
|
02 |
Identify inscribed and circumscribed shapes. |
p. 596 |
EOC, TMA |
|
03 |
Apply the perpendicular relationship between
a radius and its point of tangency. |
pp. 593-596 |
EOC, TMA |
|
04 |
Find the lengths of chords and the measure of
arcs. |
pp. 601-602 |
EOC, TMA |
|
05 |
Apply the relationships between inscribed angles
and their intercepted arcs. |
pp. 608-610 |
EOC, TMA |
|
06 |
Find the measure of angles and arcs formed by
chords, secants and tangents. |
p. 615 |
EOC, TMA |
|
07 |
Find the lengths of segments associated with
circles. |
pp. 621-622 |
EOC, TMA |
Back to Top
|
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Mathematics curriculum contact:
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